That might work - using a moisture absorber and air-tight container. You might also consider using a cardboard box and tape any seems where "bugs" could enter. A cardboard box will allow the house to breath. However, cardboard will not keep the mice away.
I've never kept a gingerbread house from one year to the next. I've read that the biggest problems are dust and allowing the house to breath. An airtight container with moisture granules might be a good solution if mice are a problem.
Good luck!
Loreta
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